Question

Three uniform sticks, each of mass m, are placed on the floor as follows: stick 1 lies along the y axis from y = 0 to y = 3.5 m , stick 2 lies along the x axis from x = 0 to x = 3.5 m , stick 3 lies along the x axis from x = 3.5 m to x =7.0 m .

A.Find the x-coordinate of the center of mass of the sticks.

B.Find the y-coordinate of the center of mass of the sticks.

C.How would the location of the center of mass be affected if the mass of the sticks were doubled? Explain

Answer 1

m1 = m2 = m3 = m

Position coordinates of center of mass of first stick

x1 = 0 , y1 = 3.5/2 = 1.75 m

Position coordinates of center of mass of second stick

x2 = 3.5/2 = 1.75 m , y2 = 0

Position coordinates of center of mass of third stick

x3 = 3.5 + (3.5/2) = 3.5 + 1.75 = 5.25 m , y3 = 0

X coordinate of System X = (m1x1 + m2x2 + m3x3)/(m1+m2+m3) = (0 + 1.75m + 5.25m)/(m+m+m)

                                                                                             = 7m/3m = 7/3 = 2.33 m

Y coordinate of System Y = (m1y1 + m2y2 + m3y3)/(m1+m2+m3)

                                     = (1.75m + 0 + 0)/(m+m+m)

                                     = 1.75m/3m = 0.583 m

(c) the center of mass is shifts in -y direction